Simplify the following expression: $ r = \dfrac{-2}{9z + 5} + \dfrac{-3}{10} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{-2}{9z + 5} \times \dfrac{10}{10} = \dfrac{-20}{90z + 50} $ Multiply the second expression by $\dfrac{9z + 5}{9z + 5}$ $ \dfrac{-3}{10} \times \dfrac{9z + 5}{9z + 5} = \dfrac{-27z - 15}{90z + 50} $ Therefore $ r = \dfrac{-20}{90z + 50} + \dfrac{-27z - 15}{90z + 50} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-20 - 27z - 15}{90z + 50} $ $r = \dfrac{-27z - 35}{90z + 50}$